This paper develops a pseudo power spectrum technique for measuring the
lensing power spectrum from weak lensing surveys in both the full sky and flat
sky limits. The power spectrum approaches have a number of advantages over the
traditional correlation function approach. We test the pseudo spectrum method
by using numerical simulations with square-shape boundary that include masked
regions with complex configuration due to bright stars and saturated spikes.
Even when 25% of total area of the survey is masked, the method recovers the
E-mode power spectrum at a sub-percent precision over a wide range of
multipoles 100<l<10000, better than the statistical errors expected for a 2000
square degree survey. The residual B-mode spectrum is well suppressed in the
amplitudes at less than a percent level relative to the E-mode. We also find
that the correlated errors of binned power spectra caused by the survey
geometry effects are not significant. Our method is applicable to the current
and upcoming wide-field lensing surveys.

This paper shows how the cosmic shear power spectra can be directly estimated from a shear map using pseudo-power spectrum methods originally developed for the CMB. A key issue is cleanly separating the E and B modes of the shear field that are mixed together by the survey window and stellar masks. These authors achieve impressive results with sub-percent errors in the estimated EE and BB power spectra for surveys covering 2000 sq. deg. (in spherical geometry) and 25 sq. deg. (in the flat-sky approximation). This is all the more impressive considering that 25% of the area in each case is removed from (simulated) stellar and bad pixel masks.

The authors note that the ~1% residual B-mode power is likely from the so-called "ambiguous" modes that arise from decomposing a spin−2 field on a finite region (described in Bunn et al. 2003). As stated in their conclusions, it will be very interesting to see how the methods for removing these ambiguous modes that have already been applied to the CMB work for cosmic shear maps. It's not at all clear to me that the methods of, e.g., Smith & Zaldarriaga (2007) will work because these require specifying a nicely apodized window to cover the masked regions. But the small-scale structure in the stellar masks makes it difficult to devise an apodized mask that still preserves a reasonable signal-to-noise ratio.

Another potential practical issue is the computational cost in computing the mode-mode coupling matrix relating the pseudo and true power spectra. It would be interesting to compare this computational cost with that required for a correlation function analysis. In particular, perhaps it will soon be feasible to undertake a Monte Carlo error analysis for cosmic shear pseudo-Cls as has been done for the CMB.